Related papers: Confidence sets in nonparametric calibration of ex…

We propose a numerical method for the valuation of European-style options under two-asset infinite-activity exponential L\'evy models. Our method extends the effective approach developed by Wang, Wan & Forsyth (2007) for the 1-dimensional…

We demonstrate and discuss nonasymptotic bounds in probability for the cost of a regression scheme with a general loss function from the perspective of the Rademacher theory, and for the optimality with respect to the average…

I propose a new type of confidence interval for correct asymptotic inference after using data to select a model of interest without assuming any model is correctly specified. This hybrid confidence interval is constructed by combining…

Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…

Confidence ellipsoids for linear regression coefficients are constructed by observations from a mixture with varying concentrations. Two approaches are discussed. The first one is the nonparametric approach based on the weighted least…

Given discrete time observations over a growing time interval, we consider a nonparametric Bayesian approach to estimation of the L\'evy density of a L\'evy process belonging to a flexible class of infinite activity subordinators. Posterior…

The use of standard statistical methods, such as maximum likelihood, is often justified based on their asymptotic properties. For suitably regular models, this theory is standard but, when the model is non-regular, e.g., the support depends…

Nonparametric series regression often involves specification search over the tuning parameter, i.e., evaluating estimates and confidence intervals with a different number of series terms. This paper develops pointwise and uniform inferences…

The problem of European-style option pricing in time-changed L\'{e}vy models in the presence of compound Poisson jumps is considered. These jumps relate to sudden large drops in stock prices induced by political or economical hits. As the…

In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive point estimation, the…

We study asymptotic properties of maximum likelihood estimators of drift parameters for a jump-type Heston model based on continuous time observations, where the jump process can be any purely non-Gaussian L\'evy process of not necessarily…

The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…

This study examines a nonparametric inference on a stationary L\'evy-driven Ornstein-Uhlenbeck (OU) process $X = (X_{t})_{t \geq 0}$ with a compound Poisson subordinator. We propose a new spectral estimator for the L\'evy measure of the…

We suggest general methods to construct asymptotically uniformly valid confidence intervals post-model-selection. The constructions are based on principles recently proposed by Berk et al. (2013). In particular the candidate models used can…

In this paper, we obtain asymptotic formulas with error estimates for the implied volatility associated with a European call pricing function. We show that these formulas imply Lee's moment formulas for the implied volatility and the…

We develop a new model selection method for the adaptive robust efficient nonparametric signal estimation observed with impulse noise which is defined by the general non Gaussian L\'evy processes. On the basis of the developed method, we…

We consider nonparametric estimation of mean regression and conditional variance (or volatility) functions in nonlinear stochastic regression models. Simultaneous confidence bands are constructed and the coverage probabilities are shown to…

We propose a new model for electricity pricing based on the price cap principle. The particularity of the model is that the asset price is an exponential functional of a jump L\'evy process. This model can capture both mean reversion and…

Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density $r_0$ and intensity $\lambda_0$. We take a nonparametric Bayesian approach to the…

We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only…